Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena

Abstract

We review methods for using time-periodic fields (e.g., laser or microwave fields) to induce non-equilibrium topological phenomena in quantum many-body systems. We discuss how such fields can be used to change the topological properties of the single particle spectrum, and key experimental demonstrations in solid state, cold atomic, and photonic systems. The single particle Floquet band structure provides a stage on which the system's dynamics play out; the crucial question is then how to obtain robust topological behaviour in the many-particle setting. In the regime of mesoscopic transport, we discuss manifestations of topological edge states induced in the Floquet spectrum. Outside the context of mesoscopic transport, the main challenge of inducing stable topological phases in many-body Floquet systems is their tendency to absorb energy from the drive and thereby to heat up. We discuss three routes to overcoming this challenge: long-lived transient dynamics and prethermalization, disorder-induced many-body localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of these regimes, and their experimental realizations.

Review paper. Supplementary information containing key technical details and derivations is included

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• Floquet Phases of Matter via Classical Prethermalization
• Unified theory to characterize Floquet topological phases by quench dynamics
• Effective Floquet Hamiltonian in the low-frequency regime
• Topological Field Theory far from Equilibrium
• Effective Floquet Hamiltonians for periodically-driven twisted bilayer graphene
• Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
• Interacting topological frequency converter
• Intrinsic dissipative Floquet superconductors beyond mean-field theory
• The Rabi problem with elliptic polarization